1. Field of the Invention
The present invention relates to a mask data correction method used for manufacturing a photomask used in photolithography in a semiconductor device manufacturing process, a photomask manufacturing method, and a computer program. Also, the present invention relates to an optical image prediction method of predicting an optical image formed by photolithography, a resist pattern shape prediction method, and a semiconductor device.
2. Description of the Related Art
(First Background Art)
Recently, in a semiconductor device, along with the requirement for a higher density, higher operation speed, and lower power consumption, a circuit pattern has been micropatterned. Therefore, in the semiconductor device manufacturing process, pattern dimensions must be controlled at high precision.
In the semiconductor device manufacturing process, a resist film is formed on a target film on which a circuit is to be formed. This resist film is irradiated with radiation to form a resist pattern, and the resist pattern serves as a sacrificial film to process the target film. As the radiation, the i ray (365 nm) of a mercury lamp, KrF laser (248 nm), ArF laser (193 nm), and the like are used. Generally, reduction-projection exposure is performed on the resist film through a photomask using ultraviolet to deep-ultraviolet light.
A projection exposure apparatus includes a combination of a large number of lenses. Some projection exposure apparatuses have a numerical aperture (NA) of nearly 0.8 on the incident side of a projection lens. However, because of an optical proximity effect (OPE), the light intensity distribution on a mask is different from that on a transferred wafer image.
Also, since a photochemical reaction which occurs when the resist film absorbs projection light, and a resolution reaction and dissolution reaction into a developing solution accompanying this photochemical reaction have nonlinear characteristics with the projection light intensity, a mask image is different from a resist pattern. The combination of this effect and the optical proximity effect is called a process proximity effect (PPE). Furthermore, since a manufacturing process such as a reactive ion etching (RIE) is performed, a target film pattern is different from a mask pattern.
Therefore, simulation is performed in consideration of the influences of the optical proximity effect and/or a resist process, or the manufacturing process, and then mask data correction called optical proximity correction (OPC) or process proximity correction (PPC) is performed to correct a mask shape so that the resist pattern or the target film pattern has a predetermined shape.
In the mask data correction process, the simulation is performed by using information which represents the characteristics of the projection exposure apparatus. As the characteristics of the projection exposure apparatus, the NA, an illumination coherency σ, a ring shielding ratio (or annular illumination shape), a projection magnification, and the like are generally used. Note that reference symbol σ denotes the ratio between the NA on the exit side of an illumination optical system and the NA on the incident side of the projection lens, which represents the size of an illumination light source.
In consideration of the resist process or the manufacturing process, a process parameter for describing the process is acquired by using shape information (typically, dimensional information) acquired from an experimentally-formed pattern. Then, by using a simulation parameter, the mask data is changed to acquire a predetermined pattern on a substrate.
Note that Jpn. Pat. Appln. KOKAI Publication No. 2002-329653 discloses a technique for measuring and correcting illuminance nonuniformity (illuminance deviation) in the exposure area of the exposure apparatus, to improve the precision of the micropattern.
(Second Background Art)
The illumination luminance distribution of the exposure apparatus is closely related to a resist pattern dimension. More specifically, the resist dimension which depends on a pattern density (periodicity) remarkably varies upon changing the size and shape of the illumination area, and the luminance distribution in the illumination area. In order to form the same dimensional resist for the plurality of patterns having different pattern densities, the mask pattern dimension must be changed in accordance with the pattern densities (i.e., dimensional correction (proximity effect correction)). Alternatively, a proximity effect correction amount must be changed in accordance with the state of the illumination luminance distribution.
In order to calculate the proximity effect correction amount, a lithography simulator program is used. The lithography simulator program loads mask pattern information, exposure apparatus information including illumination luminance information, resist information, and process information, and calculates the resist pattern dimension on the substrate.
Conventionally, in order to input the illumination luminance information to the program, the method of representing the illumination luminance distribution by using a function preset in the program, or the method of causing the program to load arbitrary luminance distribution information is available. In the former method, for example, a distribution having a uniform luminance within a predetermined range (circle, ring, or the like), or a distribution wherein the density Gaussian-functionally attenuates from the central portion to the outer peripheral portion of the illumination area can be set. In the latter method, the distribution can be set by loading the luminance data obtained by sampling the measurement results of the exposure apparatus luminance distribution, and arranging the sampled measurement results as a matrix e.g., at substantially constant intervals in the horizontal and vertical directions.
Note that Jpn. Pat. Appln. KOKAI Publication No. 2000-232057 discloses a technique for obtaining a photosensitive solution density distribution and a pattern outline in the resist film by a numerical calculation, in further consideration of a substrate structure in the optical image simulation process of setting the wavelength of exposure light, an illumination condition, a lens condition, and defocus data as input values.
Jpn. Pat. Appln. KOKAI Publication No. 2003-37050 discloses a technique for calculating the scattering of electrons irradiating a point on a resist layer, deriving the spatial distribution function of an energy storage amount corresponding to the scattering state, calculating the spatial distribution function of the overall resist layer, calculating to convert the energy storage amount into a development rate, and simulating the resist shape pattern from the development calculation.
Jpn. Pat. Appln. KOKAI Publication No. 2001-60540 discloses a technique for calculating the storage energy irradiating a point on the resist layer, dividing the distribution using a radial storage energy distribution from the calculated incident point, and predicting the resist pattern shape from the storage energy for each unit volume and the storage energy of the overall resist layer.
(Problem of First Background Art)
In the simulation process of the mask data correction, a simulation parameter which represents a process condition is superposed on the calculation result of the light intensity distribution on a substrate surface based on mask information and the exposure apparatus information. Hence, the exposure apparatus information is very important. Note that when using the exposure apparatus, the NA, σ, ring shielding ratio can be selected. However, because of errors caused by assembling and designing the exposure apparatus, the actual exposure apparatus cannot have the characteristics (more specifically, the light intensity distribution) predicted by the specific NA, σ, ring shielding ratio. In order to perform the simulation corresponding to the actual condition, the simulation must be performed using the shift of an actual exposure apparatus characteristic from an ideal exposure apparatus characteristic.
Upon calculating the process parameter on the basis of the simulation performed without using the shift of the actual exposure apparatus characteristic from the ideal exposure apparatus characteristic, generally, the process parameter has low consistency with the experimentally-acquired parameter, and includes an error from the parameter obtained by using the shift from the ideal exposure apparatus characteristic. In accordance with this process parameter, when the mask data correction is performed by the simulation without using the shift from the ideal exposure apparatus characteristic, the correction precision decreases when the experimentally-generated pattern is not similar to the pattern to be corrected.
A lens aberration of the shifts of the actual exposure apparatus characteristics from the ideal exposure apparatus characteristics is frequently studied, and this aberration is used only in the mask data correction. Alternatively, in the latest KrF or ArF exposure apparatus, a Zernike aberration coefficient is suppressed to some mλ (λ is the wavelength), and the shift of the actual exposure apparatus characteristic from the ideal exposure apparatus characteristic is very small. Also, the shift of the light intensity distribution (called a flare) is used in the mask data correction.
Also, an exposure apparatus illumination nonuniformity (to be referred to as an illumination luminance deviation hereinafter) occurs, which is the shift of the actual exposure apparatus characteristic from the design exposure apparatus characteristic, and remarkably influences the intensity distribution of the light projected on the substrate through the mask.
Kazuya Sato, et al., Proc. SPIE vol. 3679, pp. 99-107 (1999) discloses the measurement method of the illumination luminance deviation in the exposure apparatus. This literature indicates that the illumination luminance deviation changes the OPE state, and this, in turn, affects the other general pattern shape.
(Second Problem of Background Art)
Recently, along with micropatterning of a semiconductor device, the error of the illumination luminance distribution of the exposure apparatus cannot be ignored. That is, the resist pattern dimensional prediction precision is not always sufficient only by using the function in the program. In this case, the illumination luminance distribution of the exposure apparatus must be measured to predict the resist pattern dimension by using the measurement result.
However, the information amount of the luminance data input as the matrix data is too big and overloads the program. For example, when using 300 (horizontal)×300 (vertical) data, 90,000 coordinates and luminance data are held to calculate in the program. Hence, this calculation takes a long time. The information amount can be reduced by thinning the luminance data.
However, luminance information required for precisely predicting the resist pattern shape may be lost.